The impact of investment on small-cell resource allocation

We consider a heterogeneous wireless network serving two classes of users: mobile and fixed. Mobile users can only associate with macro-cells while fixed users can be served by either macro- or small-cells. Multiple service providers (SPs) can operate in the network and each has the same macro-cell infrastructure. In contrast, each SP determines a small-cell deployment density by its investment. Each SP is given a fixed total bandwidth, which is split between macro- and small-cell service, and charges a price per unit rate for each type of service. The objective of each SP is then to select the price, bandwidth split, and investment in small-cells to maximize either revenue or social welfare. We first assume a single SP and characterize the optimal strategies for both revenue and social welfare maximization. The deployment density largely depends on the per unit deployment cost of small-cells. We then consider a binary investment game in which each SP has the option of investing in a small-cell network with fixed deployment density, and show that equilibria exist in which one, none, or both SPs invest. In most cases, the pure strategy equilibria are not socially optimal. In addition, there exists asymmetric equilibrium where one SP invests in small-cells while the other doesn't. Numerical results are presented that illustrate the effect of deployment cost on small-cell investment.